It sounds like the perfect backdrop for a made-for-TV movie:

A Saudi prince's private Boeing 707 jet . . . with carpet specially woven to resemble rippling desert sand . . . a round bed covered with $50,000 worth of red fox . . . and a safe as large as an upright coffin, filled at all times with $3 million in dollars and $3 million in yen and $3 million in every other major currency in the world.

Parked on a runway in Houston last week, the plane belongs to Prince Abdullah ibn Abdul Aziz, second deputy prime minister and commander of the Saudi National Guard.

Prince Abdullah is considered something of a romantic figure in Washington. At a reception given by a former secretary of defense several years ago, His Royal Highness was smitten at first glimpse with a young woman lobbyist and tried to whisk her away that very night.

While top American officials looked and listened, the prince pleaded his case. at least, fly with him to Geneva to meet his family, he entreated.

The lady wavered.After saying no, she said yes, and then retreated back to a maybe.

The party broke up and he summoned his ministers to try to convince her that she was making a mistake.

"But American girls don't DO that," she protested.

Finally, she declined, leaving a crestfallen Prince Abdullah circling the globe on his 707, like a Flying Dutchman, still looking for his ideal American woman.

At least, if he finds her now, she will have an easier time getting on and off the jet. The plane was back in Texas recently, getting a $1.5 million automatic off-loading device installed so that the passengers won't have to wait for ground crews.

That can be a big time-saver in places like Texas where private jets can get backed up worse than commercial flights in heavily trafficked public areas.

At a recent Republican fund-raiser for Ronald Reagan in Houston, 200 private planes came bearing fat-cat contributors, and the congestion made a lot of richies late who aren't accustomed to waiting.

But even at Texas airports, the oil-rich Arabs' planes make everything else look like stripped-down, utilitarian Beechcrafts.

The Saudis recently outfitted a Boeing 747 with a complete hospital operating room, believed to be the only one of its kind in the world. Neither Boeing nor representatives of the Saudi government will disclose which member of the royal family uses the huge jet. But one source who has viewed the airborne surgical facility said this week that the plane was designed for King Khalid, who has a heart condition and travels with a surgical team.

That plane also has a circular staircase up to a dining room designed to fit beneath the standard bubble located there in a 747.

The United Arab Emirates plane, according to someone who worked on its interior, has a 21-inch seal of hammered gold and carved walnut worked into the paneling.

The same company, Customs Woodworking of Cooper, Tex., did the comparatively modest cabinetwork on Air Force I. "The American taxpayers would never allow the money to be spent like the foreign governments do," says owner Bill Runge.

In other planes, Runge has installed temperature-controlled wine cabinets, 24-karat gold showers and bidets and doorknobs inset with semi-precious stones.